We present new observations of the white dwarf sequence of the old open cluster NGC 6791. The brighter peak previously observed in the white dwarf luminosity function (WDLF) is now better delineated, and the second, fainter peak that we suggested earlier is now confirmed. A careful study suggests that we have reached the end of the WD sequence. The WDs that create the two peaks in the WDLF show a significant turn to the blue in the color-magnitude diagram. The discrepancy between the age from the WDs and that from the main-sequence turnoff remains, and we have an additional puzzle in the second peak in the WDLF. Canonical WD models seem to fail-at least at ~25% level-in reproducing the age of clusters of this metallicity. We discuss briefly possible ways of arriving at a theoretical understanding of the WDLF. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555.